Using Equation 8-7 and Table 8-1 in your text, calculate the activity coefficient for Ca in a 0.01 M solution of Ca(ClO4)2? **Table 8-1: Activity Coefficients for Aqueous Solutions at 25°C**This table provides activity coefficients for various ions in aqueous solutions at a temperature of 25°C, organized by ionic strength and charge.**Headers:**- **Ion Size (α, pm):** The effective diameter of the ion.- **Ionic Strength (μ, M):** The concentration of ions in a solution, measured in molarity (0.001, 0.005, 0.01, 0.05, 0.1 M).**Ion Charges and Values:**1. **Charge = ±1:** - **Ion:** H⁺ - **Ion Size:** 900 pm - **Activity Coefficients:** 0.900, 0.967, 0.933, 0.914, 0.860, 0.830 - Other monovalent ions include (CH₃)₄N⁺, (C₂H₅)₄N⁺, Na⁺, OH⁻, Cl⁻, etc., with ion sizes ranging from 300 to 800 pm and varying activity coefficients based on ionic strength.2. **Charge = ±2:** - **Ions:** Mg²⁺, Be²⁺ - **Ion Size:** 800 pm - **Activity Coefficients:** 0.800, 0.872, 0.755, 0.690, 0.520, 0.455 - Other divalent ions include Co²⁺, Zn²⁺, Cu²⁺, etc., with sizes from 400 to 800 pm.3. **Charge = ±3:** - **Ions:** Al³⁺, Fe³⁺, Sc³⁺, etc. - **Ion Size:** 900 pm - **Activity Coefficients:** 0.900, 0.738, 0.514, 0.445, 0.245, 0.1584. **Charge = ±4:** - **Ions:** Th⁴⁺, Zr⁴⁺, Ce⁴⁺, etc. - **Ion Size:** 1100 pm - **Activity Coefficients:** 1 To interpolate a value of \( y \), we can set up a proportion:\[\frac{\text{Unknown } y \text{ interval}}{\Delta y} = \frac{\text{known } x \text{ interval}}{\Delta x}\]Interpolation:\[\frac{0.83 - y}{0.83 - 0.67} = \frac{20 - 16}{20 - 10} \implies y = 0.766\]For \( x = 16 \), our estimate of \( y \) is 0.766.

The given solution is 0.01 M Ca(ClO4)2. Equation for the dissociation of Ca(ClO4)2(aq) is Ca(ClO4)2(aq) -----> Ca2+(aq) + 2ClO4-(aq)Since the activity coefficient depends on ionic strength, first we have to find ionic strength of 0.01 M Ca(ClO4)2 solution. Ionic strength, μ = 12*[Ca2+]*(charge of Ca)2 + [ClO4-]*(charge ofClO4)2 = 12*(0.01M)*(+2)2 + 2*0.01M*(-1)2= 12*(0.04+0.02) M= 0.03 M Ionic strength, μ = 0.03 M According to the given table, 0.03 M lies in between 0.01 M and 0.05 M. Ionic strength, μ Activity coefficient, γ Ca2+ 0.01 0.675 0.03 γ (To be calculated) 0.05 0.485 The formula for linear interpolation is: Unknown γ interval∆γ = known μ interval∆μ⇒0.485 - γ0.485-0.675 = 0.05-0.030.05-0.01⇒0.485 - γ-0.190 = 0.020.04 = 0.5⇒0.485 - γ = -0.5*0.190 = -0.095⇒ γ =0.485+0.095⇒ γ =0.580 Activity coefficient for Ca = 0.580 (Answer)